The sum of two integers is 15. Eight times the smaller integer is one less than three times the lager integer. Find the integers.

This problem should not use system of equations. I see how to set the problem up using system of equations. How do you set the problem up using one equation similar to a consecutive equation?

Question

The sum of two integers is 15. Eight times the smaller integer is one less than three times the lager integer. Find the integers.

This problem should not use system of equations. I see how to set the problem up using system of equations. How do you set the problem up using one equation similar to a consecutive equation?

jhonyy9 · Answer

try writing what you know

x +y = 15
8x -1=3y

so hope i have understood it right your exercise

loser66 · Answer

@jhonyy9 he said that not use system of equation

anonymous · Answer

Yes, the problem should not use system of equation but one equation similar to a consecutive

anonymous · Answer

Yes, I was looking at it like this 8x + 3x -1 = 15 
8x = small'
3x-1 = large
but it does not come out right

anonymous · Answer

8x +8x-1=15 is not correct 

The integers should be 4 and 11

anonymous · Answer

If you set this problem up using system of equation, you get the integer 4 and 11 and that is the answer in the book but they do not set the problem up using system of equation. They also don't show how the problem was setup.

anonymous · Answer

They are right. http://www.wolframalpha.com/input/?i=x+%2B+y+%3D+15+and+8x+-+3y+%3D+-1

anonymous · Answer

The link is the problem set up as a system of equations.

loser66 · Answer

yea, we have to solve by system of equations.

anonymous · Answer

No, there is a way to set it up not using systems of equations. The chapter the problem is in does not even touch on system of equation and they point to a consecutive example but it is not like this. The example is not. This makes perfect sense to me a system of equation but how to set it up with out using system of equation. That is what is confusing me. I just don't see it.

anonymous · Answer

Their example they point to is:
One number is four more than another number. The sum of the two numbers is sixty six. Find the two numbers

I get this one.

n + (n+4) = 66

Makes perfect sense when reading it but the other one is just not clicking.

loser66 · Answer

@ParthKohli

parthkohli · Answer

oh... yeah

anonymous · Answer

Yes, it should not be a system of equations.

parthkohli · Answer

See, if the first integer is $x$ then the larger one is represented by $\dfrac{8x + 1}{3}$

anonymous · Answer

Yes he got the smaller one and I was trying to see how he come to that conclusion

parthkohli · Answer

Huh?$$8x = 3y - 1 \Rightarrow \dfrac{8x + 1}{3} = y$$

loser66 · Answer

oh, ya,

loser66 · Answer

thanks ParthKohli

anonymous · Answer

This is not like a consecutive problem, which the book points out. I see an undstand what Parth did.

parthkohli · Answer

That's it. So$$x + \dfrac{8x + 1}{3}$$

parthkohli · Answer

$$= 15$$

loser66 · Answer

@MDoodler he used consecutive number to construct 8x+1/3

loser66 · Answer

However, it's kind of break down the system of equation. hihihi...

anonymous · Answer

so he 8x = 3y - 1 , which I see that in the word problem and then move -1 to the 8x side and divided by 3 to get y alone. I see this but why the books through the whole chapter 2 not give a single problem like this. Just makes me think they are doing something else. Anyways thanks for the help. I might post later to see what others thoughts are on the subject.

parthkohli · Answer

Exactly, a cheated a little...